If you want a tanker career, start with tankers. Schneider & Prime have tanker school and hire new drivers. Quality Carriers also hires new drivers. FFE has an oil field tanker division in Texas. Try not to waste your time with van, reefer, flatbed, if tanker is really what you want. If you like Schneider, tell the recruiter you want tanker or you will look elsewhere.
He is absolutely the funniest guy on television. I just bought seasons 1 and 2 on DVD to watch in the truck. BAZZZINGA!
Don't forget seasons 3, 4, and 5! I love that show, I can literally watch it over and over again lol.
Why are you only looking at the larger companies? Your profile doesn't say where you are at, but there are 400,000 trucking companies in the U.S. Many will hire new drivers. You don't have to work for one of the 10 biggest just because you are new. Get a phonebook and get yourself off the couch and hit the bricks. You would be surprised what you can find with some effort.
Stay away from them! Obviously they aren't a good company to drive for if they are pushing you to do something you aren't comfortable with! So once you work for them they will have you by the balls and then you will be forced to do those things. Stay away from all the mega-carriers! There are too many good companies out there to drive for without having to sacrifice yourself! You seem to be a smart individual and know your capabilities. This is your first good lesson as a new driver. NEVER DO ANYTHING YOU AREN'T COMFORTABLE WITH!!!! Don't let some moron recruiter for a mega-carrier talk you into doing it just so they can get their commission off of you! Tell them where to go!!!! Take some time to do some research and find a good smaller carrier to drive for. It may take some time and a lot more effort then just getting hired on by a mega-carrier. Good luck to you...
On a side note... I have been driving for 16 years and wouldn't take that job! The reward just isn't worth the risk!